 Physical Insight, Mathematical Modeling and AsymptoticsTing Lu ()
A chapter in A Celebration of Mathematical Modeling, 2004, pp 199-220 from Springer Abstract: Abstract We review several problems in fluid mechanics to demonstrate how physical insight of a problem leads to a simplified mathematical model, which specifies the choice of the proper scalings, the small parameters and the expansion scheme. The mathematical model in turn gives a more precise description of the insight. It defines the conditions under which the model is not applicable and the necessary refinement of the model. The model allows for a systematic derivation of the leading and higher order system of equations, identifies the initial and or/boundary conditions needed for the simplified system and derives the missing condition(s) of the leading order system of equations, if any, from the compatibility condition(s) on the next order. Special emphasis is placed on the importance of formulating the correct mathematical model relevant to the physical insight and the understanding of the physical implications. Keywords: Perturbation Methods; Boundary Layer Technique; Matched Asymptotics; Homogenization; Singular Rays. (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0427-4_11 Ordering information: This item can be ordered from DOI: 10.1007/978-94-017-0427-4_11 Access Statistics for this chapter More chapters in Springer Books from Springer |
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